“I’ve said good words about Mitch McConnell,” Durbin said Monday. “He understands the gravity of the situation in a way that John Boehner does not.”

In contrast to the government-shutdown showdown earlier this year, McConnell has played a leading role in the debt-limit negotiations.

He unveiled a plan in mid-July that would have given Obama authority to raise the debt limit, subject to congressional resolutions of disapproval. At the time, he said it was important to send the message to Social Security recipients and military families that “default is not an option.”

Some on the right, including members of Congress, attacked him, but McConnell shrugged off the salvos.

“I think he’s very important, the fact that he came up with an initial plan [shows] he understands the need to do something,” Durbin said Tuesday. “I feel he is playing a very important role in this.”

Reid said, “There are conversations going on.”

McConnell’s staff, however, say their boss has no intention of breaking with Boehner.

McConnell touted the Speaker’s plan Tuesday as a pragmatic solution. His staff claims Reid was willing to accept it over the weekend before the president reportedly rejected it. Reid’s aides vigorously dispute those assertions.

Even so, Democrats hope to take advantage of McConnell’s and Boehner’s different political situations.

McConnell is aiming to take over as Senate majority leader in 2013. To do that, Republicans would need to pick up three or four Senate seats, depending on whether Obama wins reelection.

McConnell has publicly stated his concern that Republicans could be hurt in next year’s election if Congress causes the nation to default on its obligations.

“If we go into default, [the president] will say that Republicans are making the economy worse,” he said earlier this month on Laura Ingraham’s radio show. “The president will have the bully pulpit to blame the Republicans for all of this destruction.”

Boehner, by contrast, already serves as the top leader of his chamber. He wants to keep his job, but to do so, he must maintain the support of conservatives who form the core of his conference. A compromise to raise the debt ceiling that provokes outrage among conservative activists could undermine Boehner’s future as Speaker.

Several House conservatives say they will not shy away from forcing a default, and downplay its consequences.

On Tuesday, Reid said the Speaker is captive to Tea Party lawmakers and questioned his resolve to avoid a default.

“The Tea Party is in the driver’s seat for the House Republicans now, and that’s a very, very scary thought,” Reid said.

“I believe that the Speaker would like to avoid a default, but he sure has a funny way of showing it,” he added. “He has been uncompromising.

“Based on the right-wing direction that caucus has taken, unless he decides to step back and be a statesman and not be driven by these right-wing ideologues, that’s where we’re headed,” Reid said.

Reid said Boehner’s debt plan is unacceptable because it would initially raise the debt ceiling for a short term and condition a second increase on Congress passing a major deficit-reduction deal. Reid says that will create too much uncertainty in the markets.

Boehner spokesman Michael Steel rejected that critique.

“The House will vote on a bill that is reasonable and responsible,” he said. “It was written in consultation with the Senate leadership. It can pass the House and it can pass the Senate — and the president should sign it into law.”

Democratic aides think McConnell will be willing to craft a compromise with Reid after the Senate defeats Boehner’s fallback plan, assuming the House can even pass it on Wednesday.

But a senior GOP aide said a rumor that McConnell secretly has qualms with Boehner’s plan “isn’t true.”